Inexact Newton Method via Lanczos Decomposed Technique for Solving Box-Constrained Nonlinear Systems
-
摘要: 提出了结合Lanczos分解技术不精确Newton法求解有界变量约束非线性系统.通过Lanczos分解技术解一个仿射二次模型获得迭代方向.利用内点回代线搜索技术,沿着这个方向得到一个可接受的步长.在合理的假设条件下,证明了算法的整体收敛性与局部超线性收敛速率.此外,数值结果表明了算法的有效性.
-
关键词:
- 非线性系统 /
- Lanczos方法 /
- 不精确Newton法 /
- 非单调技术
Abstract: An in exact Newton methodvia Lanczos decomposed technique was proposed for solving the box-constrained nonlinear systems.The iterative direction was obtained by solving an affine scaling quadratic modelwith Lanczos decom posed technique.By using the in terior backtracking line search technique,the acceptable trial steplength a long this direction will be found.The global convergence and fastlocal convergence rate of the proposed algorithm were established under some reasonable conditions.Furthermore,the results of the numerical expermients are reported to show the effectiveness of the proposed a lgorithm. -
[1] Coleman T F, Li Y. An interior trust-region approach for nonlinear minimization subject to bounds[J]. SIAM J Optim, 1996, 6(2): 418-445. doi: 10.1137/0806023 [2] Bellavia S, Macconi M, Morini B. An affine scaling trust-region approach to bound-constrained nonlinear systems[J]. Appl Numer Math, 2003, 44(3): 257-280. doi: 10.1016/S0168-9274(02)00170-8 [3] Jia C A, Zhu D T. An affine scaling interior algorithm via Lanczos path for solving bound-constrained nonlinear systems[J]. Applied Mathematics and Computation, 2008, 195(2): 558-575. doi: 10.1016/j.amc.2007.05.066 [4] Dembo R S, Eisenstat S C, Steihaug T. Inexact Newton methods[J].SIAM J Numer Anal, 1982, 19(2): 400-408. doi: 10.1137/0719025 [5] Shen W P, Li C. Kantorovich-type convergence criterion for inexact Newton methods[J].Appl Numer Math, 2009, 59(7): 1599-1611. doi: 10.1016/j.apnum.2008.11.002 [6] Gould Ni I M, Lucidi S, Roma M, Toint P H L. Solving the trust-region subproblem using the Lanczos method[J]. SIAM Journal on Optimization, 1999, 9(2): 504-525. doi: 10.1137/S1052623497322735 [7] Gripp R S, Lampariello F, Lucidi S.A nonmonotone line search technique for Newton’s methods[J]. SIAM J Numer Anal, 1986, 23(4): 707-716. doi: 10.1137/0723046 [8] Guo P H, Zhu D T. A nonmonotonic reduced projected Hessian method via an affine scaling interior modified gradient path for bounded-constrained optimization[J].Journal of Systems Science and Complexity, 2008, 21(1): 85-113. doi: 10.1007/s11424-008-9069-y [9] Ortega J M, Rheinboldt W C. Iterative Solution of Nonlinear Equations in Several Variables[M]. New York: Academic Press, 1970. [10] Floudas C A, Pardalos P M. Handbook of Test Problems in Local and Global Optimization[M].Dordrecht: KluwTer Academic, 1999. [11] Schittkowski K. More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems[M]. Heidelberg, Berlin: Springer-Verlag, 1981.
点击查看大图
计量
- 文章访问数: 1219
- HTML全文浏览量: 96
- PDF下载量: 742
- 被引次数: 0